Um unless I've been mistaken all this time, there is no Hike Inn parking area. It's called the Hike Inn because you have to do just that. The Inn is off of the AT approach trail from Amicalola falls to Springer. Basically you'll park at Amicalola and hike about 5 miles to the inn. Or I guess you could park at Springer and come in from that way as well. The approach trail is 9 miles. So you could hike to the inn from Amicalola then hike the rest of the way to Springer and camp there. Springer is also the start of the BMT so instead of hiking around the AT you could do some sections of the BMT.
Do you plan on going soon? Because in the fall when the leaves are in full color the approach trail is beyond beautiful. It's like something out of a movie. It reminded of The House of Flying Daggers. Epic.
"As a well spent day brings happy sleep, a well spent life brings happy death." -Da Vinci